Approximation of a Map Between One-Dimensional Teichmüller Spaces

REFERENCES

• Farkas , H. M. and Kra , I. 1991 . Riemann surfaces, , 2nd ed. New York : Springer. . [Farkas and Kra 1991], Graduate Texts in Math. 71
   Google Scholar
• Keen , L. and Series , C. 1993 . “Pleating coordinates for the Maskit embedding of the Teichmüller space of punctured tori” . Topology , 32 ( 4 ) : 719 – 749 . [Keen and Series 1993]
   Web of Science ®Google Scholar
• Keen , L. and Series , C. 1994 . “The Riley slice of Schottky space” . Proc. London Math. Soc. (3) , 69 ( 1 ) : 72 – 90 . [Keen and Series 1994]
   Google Scholar
• King , J. T. 1984 . Introduction to numerical computation New York : McGraw-Hill. . [King 1984]
   Google Scholar
• Kra , I. 1972 . Automorphic forms and Kleinian groups Reading , MA : W. A. Benjamin. . [Kra 1972]
   Google Scholar
• Kra , I. 1984 . “On cohomology of Kleinian groups, IV: The Ahlfors-Sullivan construction of holomorphic Eichler integrals” . J. Analyse Math. , 43 : 51 – 87 . [Kra 1984a]
   Web of Science ®Google Scholar
• Kra , I. 1984 . “On the vanishing of and spanning sets for Poincaré series for cusp forms” . Acta Math. , 153 : 47 – 116 . [Kra 1984b]
   Web of Science ®Google Scholar
• Kra , I. 1985 . “On algebraic curves (of low genus) defined by Kleinian groups” . Ann. Polon. Math. , 46 : 147 – 156 . [Kra 1985]
   Google Scholar
• Kra , I. 1988 . “Non-variational global coordinates for Teichmüller spaces”. ” . In Holomorphic functions and moduli II (Berkeley, 1986) Edited by: Drasin , D. 221 – 249 . New York : Springer. . [Kra 1988], Math. Sci. Res. Inst. Publ. 11
   Google Scholar
• Kra , I. 1990 . “Horocyclic coordinates for Riemann surfaces and moduli spaces, I: Teichmüller and Riemann spaces of Kleinian groups” . J. Amer. Math. Soc. , 3 : 499 – 578 . [Kra 1990]
   Google Scholar
• Kra , I. 1991 . “Cusp forms associated to rank 2 parabolic subgroups of Kleinian groups” . Proc. Amer. Math. Soc. , 111 ( 3 ) : 803 – 814 . [Kra 1991]
   Web of Science ®Google Scholar
• Lehner , J. 1964 . Discontinuous groups and automorphic functions RI : Providence. . [Lehner 1964], Mathematical Surveys 8, Amer. Math. Soc.
   Google Scholar
• Lepowsky , J. , Lindenstrauss , J. , Manin , Y. I. and Milnor , J. 1999 . “The mathematical work of the 1998 Fields medalists” . Notices Amer. Math. Soc. , 46 ( 1 ) : 17 – 26 . [Lepowsky et al. 1999]
   Google Scholar
• Maskit , B. 1974 . “Moduli of marked Riemann surfaces” . Bull. Amer. Math. Soc. (N.S.) , 80 : 773 – 777 . [Maskit 1974]
   Web of Science ®Google Scholar
• Maskit , B. 1987 . Kleinian Groups New York : Springer. . [Maskit 1987], Grundlehren der math. Wissenschaften 287
   Google Scholar
• Matsuzaki , K. and Taniguchi , M. 1998 . Hyperbolic manifolds and Kleinian groups Oxford : Clarendon Press. . [Matsuzaki and Taniguchi 1998], Oxford Mathematical Monographs
   Google Scholar
• McMullen , C. 1991 . “Cusps are dense” . Ann. of Math. (2) , 133 : 217 – 247 . [McMullen 1991a]
   Web of Science ®Google Scholar
• McMullen , C. “Rational Maps and Kleinian Groups” . Proceedings of the International Congress of Mathematicians . 1990 , Kyoto . Edited by: Satake , I. vol. II , pp. 889 – 899 . New York : Springer. . [McMullen 1991b]
   Google Scholar
• McMullen , C. 1998 . “Complex earthquakes and Teichmüller theory” . J. Amer. Math. Soc. , 11 ( 2 ) : 283 – 320 . [McMullen 1998]
   Web of Science ®Google Scholar
• Springer , G. 1957 . Introduction to Riemann Surfaces Reading , MA : Addison-Wesley. . [Springer 1957]
   Google Scholar
• Swinnerton-Dyer , H. P. F. 1974 . Analytic theory of Abelian varieties Cambridge : University Press. . [Swinnerton-Dyer 1974], London Mathematical Society lecture note series 14
   Google Scholar
• Wright , D. J. “The shape of the boundary of the Teichmüller space of once-punctured tori in Maskit's embedding” [Wright n.d.], preprint
   Google Scholar